SOLUTION: write an exponential function in {{{y=ab^x}}} passing through the points (2,1)(5,16)

Question 961247: write an exponential function in passing through the points (2,1)(5,16)
Found 2 solutions by MathLover1, stanbon:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
write an exponential function in passing through the points (,) and (,)

=> use (,), substitute and
...solve for
........eq.1

now use (,)

...solve for
......eq.2

from eq.1 and eq.2 we have
........both sides multiply by

find
........eq.1

substitute and in and you have:

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
write an exponential function in passing through the points (2,1)(5,16)
------
Solve for "a" and "b"::
y = ab^x
-----
Using (2,1) you get: 1 = ab^2
Using (5,16) you get: 16 = ab^5
-------
Dividing the bottom eq. by the top eq. you get:
16 = b^3
----
Then b = 2^4/3
-----
Solve for "a" by substituting for "b"::
1 = a*(2^(4/3)]^2
1 = a*(2^(8/3))
a = 2^(-8/3)
-----
Ans: y = (2^(-8/3))*(2^(4x/3))
y = 2^[(-8/3)+(4x/3)]
y = 2^((4x-8)/3)
y = 2^[4(x-2)/3]
y = 16^[(x-2)/3]
--------------
Cheers,
Stan H.
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